A mathematician is verifying a table of trigonometric identities for the variable α\alphaα.
Using the compound angle identity for sin(A+B)\sin(A + B)sin(A+B), derive the identity for sin2α \sin 2\alpha\,sin2α in terms of sinα \sin \alpha\,sinα and cosα\cos \alphacosα.
Using the compound angle identity for cos(A+B)\cos(A + B)cos(A+B), derive the identity for cos2α \cos 2\alpha\,cos2α in terms of sinα \sin \alpha\,sinα and cosα\cos \alphacosα.
Hence, write cos2α \cos 2\alpha\,cos2α as an expression containing only the term cosα\cos \alphacosα.
Hence, write cos2α \cos 2\alpha\,cos2α as an expression containing only the term sinα\sin \alphasinα.
Utilize the addition formula for tan(A+B)\tan(A + B)tan(A+B) to find an expression for tan2α \tan 2\alpha\,tan2α in terms of tanα\tan \alphatanα.
Practise Edexcel A Level Maths Trigonometry and Modelling with exam-style questions for A Level Maths. 100 questions covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.